Fetching the paper…
Reading the bibliography…
We provide a new algorithm for generating the Baker--Campbell--Hausdorff (BCH) series $Z = \log(\e^X \e^Y)$ in an arbitrary generalized Hall basis of the free Lie algebra $\mathcal{L}(X,Y)$ generated by $X$ and $Y$.
Alternant and continuous groups
H.F. Baker · 1905
Earlier work this paper cites.
Die symbolische Exponential Formel in der Gruppen theorie
F. Hausdorff · 1906
Earlier work this paper cites.
Evaluation of the coefficients of the Campbell–Hausdorff formula
E.B. Dynkin · 1947
Earlier work this paper cites.
On the exponential solution of differential equations for a linear operator
W. Magnus · 1954
Earlier work this paper cites.
The formal power series for log ( e x e y ) \log(\mathrm{e}^{x}\mathrm{e}^{y})
K. Goldberg · 1956
Earlier work this paper cites.
The Baker–Hausdorff formula and a problem in Crystal Physics
G.H. Weiss and A.A. Maradudin · 1962
Earlier work this paper cites.
Handbook of Mathematical Functions
M. Abramowitz and I.A. Stegun · 1965
Earlier work this paper cites.
On expanding the exponential
K. Kumar · 1965
Earlier work this paper cites.
Expansion of the Campbell–Baker–Hausdorff formula by computer
R.D. Richtmyer and S. Greenspan · 1965
Earlier work this paper cites.
Exponential operators and parameter differentiation in quantum physics
R.M. Wilcox · 1967
Earlier work this paper cites.
Bases des algèbres de Lie et série de Hausdorff
J. Michel · 1974
Earlier work this paper cites.
Linear Differential Equations with Periodic Coefficients
V.A. Yakubovich and V.M. Starzhinskii · 1975
Earlier work this paper cites.
Lie series and invariant functions for analytic symplectic maps
A. J. Dragt and J. M. Finn · 1976
Earlier work this paper cites.
On the convergence of exponential operators—the Zassenhaus formula, BCH formula and systematic approximants
M. Suzuki · 1977
Earlier work this paper cites.
Algèbres de Lie Libres et monoïdes libres
X.G. Viennot · 1978
Earlier work this paper cites.
Lie Algebras
N. Jacobson · 1979
Earlier work this paper cites.
Cyclic relations and the Goldberg coefficients in the Campbell–Baker–Hausdorff formula
R.C. Thompson · 1982
Earlier work this paper cites.
Combinatorics on Words
M. Lothaire · 1983
Cited alongside, same era.
Lie Groups, Lie Algebras, and Their Representations
V. S. Varadarajan · 1984
Cited alongside, same era.
Mobius Functions, Incidence Algebras and Power-Series Representations
A. Dür · 1986
Cited alongside, same era.
Espaces symétriques et méthode de Kashiwara–Vergne
F. Rouvière · 1986
Cited alongside, same era.
Proof of a conjectured exponential formula
R.C. Thompson · 1986
Cited alongside, same era.
Numerical values of Goldberg’s coefficients in the series for log ( e x e y ) \log(\mathrm{e}^{x}\,\mathrm{e}^{y})
M. Newman and R.C. Thompson · 1987
Cited alongside, same era.
Lie Groups and Lie Algebras. Semester V of Lectures in Geometry
M. Postnikov · 1994
Later among the works it cites.
Numerical Hamiltonian Problems
J. M. Sanz-Serna and M. P. Calvo · 1994
Later among the works it cites.
Foundations of Lie Theory and Lie Transformation Groups
V.V. Gorbatsevich, A.L. Onishchik, and E.B. Vinberg · 1997
Later among the works it cites.
Magnus and Fer expansions for matrix differential equations: the convergence problem
S. Blanes, F. Casas, J.A. Oteo, and J. Ros · 1998
Later among the works it cites.
On the solution of linear differential equations in Lie groups
A. Iserles and S. P. Nørsett · 1999
Later among the works it cites.
Higher-order methods for simulations on quantum computers
A.T. Sornborger and E.D. Stewart · 1999
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
R.C. Thompson · 1988
Cited alongside, same era.
Dynkin’s method of computing the terms of the Baker–Campbell–Hausdorff series
A. Bose · 1989
Cited alongside, same era.
Lie groups and Lie algebras
N. Bourbaki · 1989
Cited alongside, same era.
Hopf-algebraic structure of families of trees
R. Grossman and R.G. Larson · 1989
Cited alongside, same era.
Convergence domains for the Campbell-Baker-Hausdorff formula
M. Newman, W. So, and R.C. Thompson · 1989
Cited alongside, same era.
Convergence proof for Goldberg’s exponential series
R.C. Thompson · 1989
Cited alongside, same era.
Lie-group methods
A. Iserles, H. Z. Munthe-Kaas, S. P. Nørsett, and A. Zanna · 2000
Later among the works it cites.
A simple expression for the terms in the Baker–Campbell–Hausdorff series
M.W. Reinsch · 2000
Later among the works it cites.
Splitting methods
R.I. McLachlan and R. Quispel · 2002
Later among the works it cites.
On backward error analysis and Nekhoroshev stability in the numerical analysis of conservative systems of ODEs
P.C. Moan · 2002
Later among the works it cites.
Combinatorics of rooted trees and Hopf algebras
M.E. Hoffman · 2003
Later among the works it cites.
On the convergence and optimization of the Baker–Campbell–Hausdorff formula
S. Blanes and F. Casas · 2004
Later among the works it cites.
A software package for Lie algebraic computations
M. Torres-Torriti and H. Michalska · 2005
Later among the works it cites.
Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations
E. Hairer, Ch. Lubich, and G. Wanner · 2006
Later among the works it cites.
The Hopf algebra of rooted trees, free Lie algebras, and Lie series
A. Murua · 2006
Later among the works it cites.
Sufficient conditions for the convergence of the Magnus expansion
F. Casas · 2007
Later among the works it cites.
Magnus expansion: mathematical study and physical applications, 2008
S. Blanes, F. Casas, J.A. Oteo, and J. Ros · 2008
Closest in time.